163 research outputs found

    Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions

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    We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster algorithm in one-dimensional subspaces of the configuration space. This improvement allows us to study classical systems up to L=512L=512. Based on the new algorithm we give evidence for the presence of strongly anomalous scaling for periodic boundary conditions which is much worse than anticipated before. We propose and study alternative boundary conditions for the compass model which do not make use of extended configuration spaces and show that they completely remove the problem with finite-size scaling. In the last part, we apply these boundary conditions to the quantum problem and present a considerably improved estimate for the critical temperature which should be of interest for future studies on the compass model. Our investigation identifies a strong one-dimensional magnetic ordering tendency with a large correlation length as the cause of the unusual scaling and moreover allows for a precise quantification of the anomalous length scale involved.Comment: 10 pages, 8 figures; version as publishe

    Make life simple: unleash the full power of the parallel tempering algorithm

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    We introduce a new update scheme to systematically improve the efficiency of parallel tempering simulations. We show that by adapting the number of sweeps between replica exchanges to the canonical autocorrelation time, the average round-trip time of a replica in temperature space can be significantly decreased. The temperatures are not dynamically adjusted as in previous attempts but chosen to yield a 50% exchange rate of adjacent replicas. We illustrate the new algorithm with results for the Ising model in two and the Edwards-Anderson Ising spin glass in three dimensionsComment: 4 pages, 5 figure

    Universality of the evaporation/condensation transition

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    AbstractBy making use of the well-known lattice-gas interpretation, we investigated the evaporation/condensation transition through Monte Carlo simulations of the square lattice Ising model with nearest-neighbour couplings and periodic boundary conditions. The particle density can be varied by choosing different fixed magnetisations. In the analysis of our data we followed recent analytical work by Biskup et al. [Europhys. Lett. 60 (2002) 21], who also used the Ising model to study liquid-vapour systems at a fixed excess ÎŽN of particles above the ambient gas density in the limit of large system sizes. By identifying a dimensionless parameter Δ(ÎŽN), they showed that for Δ<Δc all excess is absorbed in background fluctuations (“evaporated” system), while for Δ>Δc a single large droplet of the dense phase occurs (“condensed” system). Besides the threshold value Δc also the fraction λ of excess particles forming the droplet is given explicitly.To test the applicability of these asymptotic results to practically accessible system sizes, we measured the volume of the largest minority droplet, corresponding to a fluid drop, for various L×L lattices with L=40,
,640. Using analytic values for the spontaneous magnetisation m0, the susceptibility χ and the Wulff interfacial free-energy density τW for the infinite system, we were able to determine Δc and λ numerically in very good agreement with the theoretical prediction. We also discuss the associated free-energy barrier and its implication for multimagnetical simulations, and put these findings into context with the related droplet/strip transition respectively barrier

    Force-clamp spectroscopy of reversible bond breakage

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    We consider reversible breaking of adhesion bonds or folding of proteins under the influence of a constant external force. We discuss the stochastic properties of the unbinding/rebinding events and analyze their mean number and their variance in the framework of simple two-state models. In the calculations, we exploit the analogy to single molecule fluorescence and particularly between unbinding/rebinding and photon emission events. Environmental fluctuation models are used to describe deviations from Markovian behavior. The second moment of the event-number distribution is found to be very sensitive to possible exchange processes and can thus be used to identify temporal fluctuations of the transition rates.Comment: 8 pages, 4 figure

    Phase transition and dynamical-parameter method in U(1) gauge theory

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    Monte Carlo simulations of the 4-dimensional compact U(1) lattice gauge theory in the neighborhood of the transition point are made difficult by the suppression of tunneling between the phases, which becomes very strong as soon as the volume of the lattice grows to any appreciable size. This problem can be avoided by making the monopole coupling a dynamical variable. In this manner one can circumvent the tunneling barrier by effectively riding on top of the peaks in the energy distribution which meet for sufficiently large monopole coupling. Here we present an efficient method for determining the parameters needed for this procedure, which can thus be implemented at low computational cost also on large lattices. This is particularly important for a reliable determination of the transition point. We demonstrate the working of our method on a 16^4 lattice. We obtain an equidistribution of configurations across the phase transition even for such a relatively large lattice size.Comment: 11 pages, latex, 2 figures included, uuencode

    Phase structure and monopoles in U(1) gauge theory

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    We investigate the phase structure of pure compact U(1) lattice gauge theory in 4 dimensions with the Wilson action supplemented by a monopole term. To overcome the suppression of transitions between the phases in the simulations we make the monopole coupling a dynamical variable. We determine the phase diagram and find that the strength of the first order transition decreases with increasing weight of the monopole term, the transition thus ultimately getting of second order. After outlining the appropriate topological characterization of networks of currents lines, we present an analysis of the occurring monopole currents which shows that the phases are related to topological properties.Comment: 22 pages (latex), 14 figures (available upon request), BU-HEP 94-
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